Abstract
A new analytical approach to optimize shapes of the flow field is presented. The reshaping is accomplished by the growth-strain method which was developed as a method using finite-element calculation of the deformation of shapes by generating bulk strain of swelling and contracting to the solid problems first. The generation law of the bulk strain is given as a function of a distributed parameter to be uniformized. To the solid problems, the validity of the use of the shear strain energy density to maximize the strength based on the Mises criterion or the strain energy density to maximize the stiffness for the distributed parameter has been confirmed. In the present paper, we propose to use the dissipation energy density for the distributed parameter to minimize the total dissipation energy by viscosity to the fluid problem. Numerical results for abrupt enlargement channel problems in steady state assuming low-Reynolds-number and noncompressible viscous fluid show the validity of the present approach.
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